What are your insights on The Hardest Logic Puzzle Ever?

[mathassistant]

Hello! I’m an assistant of a mathematical scientific researcher, and my research programme evolves around finding and developing all the (possible) solutions regarding all unsolved mathematical, logic, exact, and IQ puzzles ever created. If you search on the internet for: “The hardest unsolved logic math/iq puzzle/problem ever possible”. You would find the well-known "The Hardest Logic Puzzle Ever" (https://en.wikipedia.org/wiki/The_Hardest_Logic_Puzzle_Ever). I would like to gather some of your thoughts around this puzzle.

Quote:
This puzzle involves three gods, A, B, and C, who are named True, False, and Random. True always speaks truly, False always speaks falsely, and Random's responses are completely random. The goal is to determine the identities of A, B, and C by asking three yes-no questions, with each question directed at only one god. The gods respond in their own language, where the words for yes and no are da and ja, in some order, and we do not know which word corresponds to which answer.
End quote.

The proposed solution on Wikipedia assumes that one of the gods must answer a factual question truthfully, leading to the conclusion that "ja" corresponds to "yes" and "da" corresponds to "no." However, this assumption is not valid within the constraints of the puzzle, as Random's responses are completely random, and there is no guarantee that a factual question will elicit a truthful response.

Furthermore, the solution on Wikipedia violates the rule that each question must be directed at only one God. In the proposed solution, the same god is asked the third question, which is not in accordance with the puzzle's requirements.

Considering the difficulty of this puzzle, I have a few questions for you. Given that “puzzle” is a puzzle related to:

• Math
• Logic
• Insight
• Strategic
• Tactic
• Intelligence
• Exact

1. Is it ever possible that a harder, unsolved puzzle compared to "The Hardest Logic Puzzle Ever" exists? If so, what makes it more challenging?Is there a definitive solution to "The Hardest Logic Puzzle Ever"?
2. Are there any alternative valid solutions? Because based on all our research, the “solutions” available are all the same type (which are all false because of violations of the rules or assumptions).
3. If there is a solution, can a valid truth table be constructed to represent the possible answers of the gods and their identities?

I would greatly appreciate your insights and any additional information you can provide regarding the puzzle. Your contributions will aid our ongoing research into unsolved mathematical, logical, and IQ puzzles.

 

[pasmith]

Furthermore, the solution on Wikipedia violates the rule that each question must be directed at only one God. In the proposed solution, the same god is asked the third question, which is not in accordance with the puzzle's requirements.

I disagree. I believe the problem requires that each question must be addressed to a particular god, in the sense that you cannot address the same question to multiple gods and compare responses (well, you can, but each asking of the question would count towards the limit of three questions). But there is no restriction that a god who has already been asked a question cannot be asked further questions.

I don't know if the problem is actually solvable if it is interpreted as you assume.

 

[mathassistant]

I disagree. I believe the problem requires that each question must be addressed to a particular god, in the sense that you cannot address the same question to multiple gods and compare responses (well, you can, but each asking of the question would count towards the limit of three questions). But there is no restriction that a god who has already been asked a question cannot be asked further questions.

I don't know if the problem is actually solvable if it is interpreted as you assume.

Hi, thank you for your reply. I indeed misinterpreted the rule on the Wikipedia page. However, I personally think asking a god the same question twice is not a good strategy, because if you turn out to be asking random twice, one is done for.

You did mention that you 'don't know if the problem is actually solvable if it is interpreted as you assume'. Which is interesting, would you perhaps have a clue on how one would go about solving that puzzle? I've not seen any solution for it so far.